Sadly the last Govt made a right mess with the change of the main bike test in 2 parts.
Do your CBT which is approx £90 - £100.
As you are over 21 yes you can do your Direct Access, but it means paying out £500 - £1000 for a 4 or 5 day course where you do your intensive training on a 500cc or 600 cc bike from 9am - 4pm for those days and then take the test on the last day. However some people have to travel 50 - 60 miles with the instructor to do the off road hazard swerve test on a test centre built for that purpose.
However the new test is in 2 parts as you have to do the off road hazard swerve test and then do the main road test.
This came in to play a few years back, however there have been no end of accidents on the off road hazard swerve test that the Govt have been advised to change the test back to the old Direct Access method.
So what I would advise you to do, is
a) Get provisional motorcycle entitlement on your licence if you haven't already got it.
b) Take your motorcycle theory test - Yes you have to take it is the law, even if you took the driving theory test.
c) Do your CBT on a 125 it is vaild for 2 years so you can ride a bike no bigger than a 125 for 2 years on L plates (Not allowed to carry pillion)
d) Wait until the DfT change the bike test back to what it was before then take your Direct Access on a 500 or 600 bike, which should be done by then.
After 2 years is up, if you wish you can re do your CBT assuming you have not taken your main bike test. Which is new as you couldn't years ago, as back then if you didn't take your test within that 2 years, you had to wait another 2 years to re take your CBT and then do your test.
I did my old DAS with Circuit Based Training when they were at Donington Park. They are now at Mallory Park.